Hadron Structure from LQCD - Oak Ridge Leadership ... · Hadron Structure from LQCD Kostas Orginos College of William and Mary JLAB OLCF April 29, 2013 Page 1 of 6 CASA Tracking Number:

Hadron Structure from LQCDKostas Orginos

College of William and MaryJLAB

OLCF

April 29, 2013

Page 1 of 6 CASA Tracking Number:

CASA Publications Policy

1.

1.

1.

CASA Tracking Number: CASA01000

Revision Number: Rev. 1; October 26, 2001

Document Custodian: Yuhong Zhang

1.0 CASA Publications

For the purposes of this policy, CASA publications are separated into four groups.

Publications are assigned to a group based on the type of publication, whether or not the

publication will be externally viewable (i.e., viewable by non-JLab personnel), and the

level of review that the publication receives. The publication groups, which are detailed

further in the following paragraphs, are as follows.

!"

!"

!"

!"

!"

!"

!"

!"

!"

!"

Group 1 Publications – Externally viewable, reviewed per Admin. Manual

Section 702

Group 2 Publications – Externally viewable (but preceded by a popup

disclaimer), reviewed by CASA Director

Group 3 Publications – Internally viewable only, reviewed by CASA

Director, available in orginal format for potential use as part of other works

Group 4 Publications – Internally viewable only, no review

1.1 Group 1 Publications

Group 1 publications must be reviewed per Administrative Manual 702. These

publications will be maintained by a laboratory organization as noted below. Group 1

publications will not change over time. If a publication is overtaken by events, the listing

should change from a URL to a text referral that provides appropriate information. The

CASA Webmaster will maintain a comprehensive listing of Group 1 Publications on the

CASA web site, including the following.

Links to publications maintained by JLab Library:

Peer reviewed journal articles (links to journals)

Conference proceedings (links or .pdf files, as copyright allows)

Links and publications maintained by the CASA Webmaster:

Technical results (e.g., links to arXiv.org, a.k.a. xxx.lanl.gov, before formal

publication)

CEBAF and FEL spec sheets

Presentation viewgraphs (e.g., USPAS and talks from invited speakers)

Links to things maintained offsite to which CASA members contributed

(e.g., Hall D CDR, ERL proposal, etc.)

Monday, April 29, 13

Hadron StructureImportance:

How are nucleons made up from the fundamental degrees of freedom (quarks and gluons)

Understand the charge and magnetization distributions in the nucleon

Complement key elements of DOEs experimental programs

quark distributions HERMES, Fermilab, LHC

form factors and GPDs: JLab

Contributions to the nucleon spin: JLab RHIC-spin, future EIC

Transverse momentum dependent distributions: JLab, RHIC-spin, Fermilab,future EIC

JLab @ 12 GeV


Relativistic Heavy Ion Collider

LHC

LHCProton structure


Relativistic Heavy Ion Collider

LHC

LHCProton structure


Large Hadron ColliderLHC

LHC

Probe the fundamental forces in nature


Year # Milestone 2012 HP7 Measure the electromagnetic excitations of low-lying baryon states (<2 GeV) and their transition form factors over the

range Q2=0.1–7 GeV2 and measure the electro- and photo-production of final states with one and two pseudoscalar mesons.

2012 HP11 Measure the helicity-dependent and target-polarization-dependent cross-section differences for Deeply Virtual Compton Scattering (DVCS) off the proton and the neutron in order to extract accurate information on generalized parton distributions for parton momentum fractions, x, of 0.1 – 0.4, and squared momentum transfer, t, less than 0.5 GeV2 .

2013 HP8 Measure flavor-identified q and q contributions to the spin of the proton via the longitudinal-spin asymmetry of W production.

2013 HP12 Utilize polarized proton collisions at center of mass energies of 200 and 500 GeV, in combination with global QCD analyses, to determine if gluons have appreciable polarization over any range of momentum fraction between 1 and 30% of the momentum of a polarized proton.

2014 HP9 Perform lattice calculations in full QCD of nucleon form factors, low moments of nucleon structure functions and low moments of generalized parton distributions including flavor and spin dependence.

2014 HP10 Carry out ab initio microscopic studies of the structure and dynamics of light nuclei based on two-nucleon and many-nucleon forces and lattice QCD calculations of hadron interaction mechanisms relevant to the origin of the nucleon-nucleon interaction.

2015 HP13 Test unique QCD predictions for relations between single-transverse spin phenomena in p-p scattering and those observed in deep-inelastic lepton scattering

2018 HP14 Extract accurate information on spin-dependent and spin-averaged valence quark distributions to momentum fractions x above 60% of the full nucleon momentum

2018 HP15 The first results on the search for exotic mesons using photon beams will be completed.

NSAC Performance Measures in Hadronic Physics


We study strong interactions using the worlds largest computers


QCD9. Quantum chromodynamics 25

!"## !"#$ !"#%! (" )& '

!"#$%&'(#)*+#,,(-./

012))34)*5678/)

#9:.-#;<)*5678/

012))=.,<)*578/

.>.?)=.,<)@)<AB<)*5578/)

.+.-,$&C.#%)D(,<)*5678/)

.>.?)=.,<)@)<A#B.<)*5578/)

$):.-#;<)*578/

!E0 ! (" ) = 0.1184 ± 0.0007< F

!"#

!"$

!"%

!"(

!")

!&*+,-

# #! #!!,*./012

G.#H;)!"#$%&'(#.>.?))I''(A(+#,(&'0..B)1'.+#<,(-)2-#,,.$('J

K"+;)4LLM

Figure 9.2: Left: Summary of measurements of !s(M2Z), used as input for the

world average value; Right: Summary of measurements of !s as a function of therespective energy scale Q. Both plots are taken from Ref. 172.

9.4. Acknowledgments

We are grateful to S. Bethke, J. Butterworth, M. Cacciari, L. del Debbio, P. Gambino,A. Kronfeld, M. d’Onofrio, S. Sharpe, D. Treille, N. Varelas, M. Wobisch, W.M. Yao,C.P. Yuan, and G. Zanderighi for their suggestions and comments.

References:1. R.K. Ellis, W.J. Stirling, and B.R. Webber, “QCD and collider physics,” Camb.

Monogr. Part. Phys. Nucl. Phys. Cosmol. 81 (1996).2. G. Dissertori, I.G. Knowles, and M. Schmelling, “High energy experiments and

theory,”” Oxford, UK: Clarendon (2003).3. R. Brock et al., [CTEQ Collaboration], Rev. Mod. Phys. 67, 157 (1995), see also

http://www.phys.psu.edu/!cteq/handbook/v1.1/handbook.pdf.4. J. Smit, “Introduction to quantum fields on a lattice: A robust mate,” Cambridge

Lect. Notes Phys. 15 (2002), p. 1.5. T. DeGrand and C.E. Detar, Lattice methods for quantum chromodynamics,World

Scientific (2006).6. “Perspectives in Lattice QCD,” Proceedings of the Workshop, Nara International

Seminar House (2005), Ed. Y. Kuramashi, World Scientific 2008.7. T. Onogi, arXiv:0906.2344 [hep-ph].8. D. d’Enterria, arXiv:0902.2488 [nucl-ex].9. T. van Ritbergen, J.A.M. Vermaseren, and S.A. Larin, Phys. Lett. B400, 379

(1997) [arXiv:hep-ph/9701390].10. M. Czakon, Nucl. Phys. B710, 485 (2005) [arXiv:hep-ph/0411261].11. Y. Schroder and M. Steinhauser, JHEP 0601, 051 (2006) [arXiv:hep-

ph/0512058].

January 28, 2010 12:02

The theory of strong interactions

Coupling constant changes with scale

Coupling constant becomes weak at high energies

Characteristic scale arises Λqcd

αs (Λqcd)~ 1

Politzer, Gross, Wilczek 2004 Nobel prizeMonday, April 29, 13

Low energy regimeInteraction is strong

Analytic calculations not under control

Confinement

Spontaneous chiral symmetry breaking

pions: Nambu-Goldstone bosons

Nambu 2008 Nobel prize

9. Quantum chromodynamics 25

!"## !"#$ !"#%! (" )& '

!"#$%&'(#)*+#,,(-./

012))34)*5678/)

#9:.-#;<)*5678/

012))=.,<)*578/

.>.?)=.,<)@)<AB<)*5578/)

.+.-,$&C.#%)D(,<)*5678/)

.>.?)=.,<)@)<A#B.<)*5578/)

$):.-#;<)*578/

!E0 ! (" ) = 0.1184 ± 0.0007< F

!"#

!"$

!"%

!"(

!")

!&*+,-

# #! #!!,*./012

G.#H;)!"#$%&'(#.>.?))I''(A(+#,(&'0..B)1'.+#<,(-)2-#,,.$('J

K"+;)4LLM

Figure 9.2: Left: Summary of measurements of !s(M2Z), used as input for the

world average value; Right: Summary of measurements of !s as a function of therespective energy scale Q. Both plots are taken from Ref. 172.

9.4. Acknowledgments

We are grateful to S. Bethke, J. Butterworth, M. Cacciari, L. del Debbio, P. Gambino,A. Kronfeld, M. d’Onofrio, S. Sharpe, D. Treille, N. Varelas, M. Wobisch, W.M. Yao,C.P. Yuan, and G. Zanderighi for their suggestions and comments.

References:1. R.K. Ellis, W.J. Stirling, and B.R. Webber, “QCD and collider physics,” Camb.

Monogr. Part. Phys. Nucl. Phys. Cosmol. 81 (1996).2. G. Dissertori, I.G. Knowles, and M. Schmelling, “High energy experiments and

theory,”” Oxford, UK: Clarendon (2003).3. R. Brock et al., [CTEQ Collaboration], Rev. Mod. Phys. 67, 157 (1995), see also

http://www.phys.psu.edu/!cteq/handbook/v1.1/handbook.pdf.4. J. Smit, “Introduction to quantum fields on a lattice: A robust mate,” Cambridge

Lect. Notes Phys. 15 (2002), p. 1.5. T. DeGrand and C.E. Detar, Lattice methods for quantum chromodynamics,World

Scientific (2006).6. “Perspectives in Lattice QCD,” Proceedings of the Workshop, Nara International

Seminar House (2005), Ed. Y. Kuramashi, World Scientific 2008.7. T. Onogi, arXiv:0906.2344 [hep-ph].8. D. d’Enterria, arXiv:0902.2488 [nucl-ex].9. T. van Ritbergen, J.A.M. Vermaseren, and S.A. Larin, Phys. Lett. B400, 379

(1997) [arXiv:hep-ph/9701390].10. M. Czakon, Nucl. Phys. B710, 485 (2005) [arXiv:hep-ph/0411261].11. Y. Schroder and M. Steinhauser, JHEP 0601, 051 (2006) [arXiv:hep-

ph/0512058].

January 28, 2010 12:02


Particle masses

Can we calculate the dimensionless constants A ?

Quantum dynamics of strong interactions generates the mass of the visible matter

m = A Λqcd

(Hadrons)


What does it take?Hadronic Scale: 1fm ~ 1x10-13 cm

Lattice spacing << 1fm

take a=0.1fm

Lattice size La >> 1fm

take La = 6fm

Lattice 644

Gauge degrees of freedom: 8x4x644 = 5.4x108

colordimensions

sites


Monte Carlo Integration

!O" =1

Z

!

"

µ,x

dUµ(x) O[U, D(U)!1] det#

D(U)†D(U)$nf /2

e!Sg(U)



!O" =1

Z

!

"

µ,x


D(U)†D(U)$nf /2

e!Sg(U)



!O" =1

Z

!

"

µ,x


D(U)†D(U)$nf /2

e!Sg(U)



!O" =1

Z

!

"

µ,x


D(U)†D(U)$nf /2

e!Sg(U)



!O" =1

Z

!

"

µ,x


D(U)†D(U)$nf /2

e!Sg(U)


Monte Carlo Integration!O" =

1

Z

!

"

µ,x


D(U)†D(U)$nf /2

e!Sg(U)

�O⇥ =1N

N�

i=1

O(Ui)Monte Carlo Evaluation

Statistical error1�N


Realistic CalculationsInclude the vacuum polarization effects

2 light (up down) 1 heavy (strange)

... and ... 1 very heavy (charm)

Finite VolumeCompute in multiple and large volumes

Continuum LimitCompute with several lattice spacings

Quark massesCompute with several values for the quark massesStudy quark mass dependence of QCDPhysical light (up down) quark masses


Need big computers to these calculations

Ken Wilson @ Lattice ’89: “I still believe an extraordinary increase in computer power (108 is not enough) and equally powerful algorithmic advances will be necessary before a full interaction with experiment takes place”


Algorithm Improvements

Hybrid Monte Carlo (HMC)

Stochastic sampling of the field configuration space

Improved representation of vacuum polarization effects

Calculation of fermionic observables

Solve the Dirac equation

Preconditioned solvers (eigCG), multi-grid, ...

D(U)� = �


0 10 20 30 40 50 60 70 80 90

quark mass [MeV]

0.01

0.1

1

10

100

N ops [

Tflo

ps x

yea

r]

HMC ’01DD-HMC ’04deflated DD-HMC ’07

physical point

Improved HMC

[Luscher 0710.5417]

Uses an GCR with an AMG preconditioner

[Luscher 0706.2298v4]

Chronology reduces the refresh of the preconditioner

Nearly removes critical slowing down

Lattice 323 x 64 a = 0.08fm

plot by M. Luscher 1002.4232v2


GPDsy

xz

p

xp

Qz 1~⊥δ

⊥r

0⊥r

),( ⊥rxf

1

y

xz

0⊥r

p

f x( )

1

xp

Qz 1~⊥δ

x

y

xz

⊥r

)( ⊥rρ

0⊥r

p

x

Form FactorsParton Distribution

functionsGeneralized Parton

Distribution functions

X. Ji, D. Muller, A. Radyushkin (1994-1997)


Axial Charge

QCDSF arXiv:1302.2233

• Experimentally measured precisely gA = 1.2701 (25)

• Lattice calculations underestimate it

• Recent work with better control of the systematics seems promising (QCDSF, LHPC, RBC/UKQCD)


Form Factors

Alexandrou et al arXiv:1303.5979

Results from QCDSF, LHPC, RBC/UKQCD, ETM-QCD


The nucleon sigma term

• Dark Matter search experiments

• Controls uncertainty of hadronic uncertainties in dark matter cross sections for a large class of models

• LQCD determinations of the sigma term may prove important

�l ⌘ mlhN |uu+ dd|Ni �s ⌘ mshN |ss|Ni


Nucleon Sigma Term‡‡

‡‡

‡‡

‡‡

ÊÊ

ÊÊ

ÊÊ

ÊÊ

ÊÊ

ÊÊ

ÊÊ

ÊÊ

ÊÊ

ÊÊ

0 40 80 120 160

0 40 80 120 160JLQCD 2008JLQCD 2010QCDSF 2011Young & Thomas 2009Toussaint & Freeman 2009Martin-Camalich et al. 2010Dürr et al. 2011QCDSF-UKQCD 2011Freeman & Toussaint 2012Shanahan et al. 2012JLQCD 2012Ren et al. 2012Engelhardt 2012

ss HMeVL

ÚÚ

ÚÚ

‡‡

‡‡

‡‡

‡‡

‡‡

‡‡

‡‡

‡‡

‡‡

ÊÊ

ÊÊ

ÊÊ

ÊÊ

ÊÊ

ÊÊ

ÊÊ

0 20 40 60 80 100

0 20 40 60 80 100Fukugita et al. 1995Dong et al. 1996SESAM 1998Leinweber et al. 2000Leinweber et al. 2003Procura et al. 2003Procura et al. 2006ETM 2008JLQCD 2008QCDSF 2011QCDSF 2012Young & Thomas 2009PACS-CS 2009Martin-Camalich et al. 2010Dürr et al. 2011QCDSF-UKQCD 2011Shanahan et al. 2012Ren et al. 2012

sl HMeVLYoung et al. arXiv:1301.1765


Scalar and Tensor charges

• Search for new physics with precision measurements of Ultra Cold Neutrons decays

• The scalar and tensor iso-vector charges of the neutron are required to ~10%

Gupta et al. arXiv:1110.6448

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.7

0.8

0.9

1.0

1.1

1.2

Mπ2 (GeV2)

g T2+

1f

●

●● ● ●

●

●

●● ● ●

●

● RBC 2+1f

LHPC 2+1f

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.7

0.8

0.9

1.0

1.1

1.2

Mπ2 (GeV2)

g T2+

1f

●

●● ● ●

●

●

●● ● ●

●

● RBC 2+1f

LHPC 2+1f


Scalar and Tensor charges

• Search for new physics with precision measurements of Ultra Cold Neutrons decays

• The scalar and tensor iso-vector charges of the neutron are required to ~10%

Gupta et al. arXiv:1110.6448

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.6

0.8

1.0

1.2

Mπ2 (GeV2)

g S2+

1f

●

●

●

●●

●

●

●

● Anisoclover 2+1fMixed action 2+1f

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.6

0.8

1.0

1.2

Mπ2 (GeV2)

g S2+

1f

●

●

●

●●

●

●

●

● Anisoclover 2+1fMixed action 2+1f


GPDs: Lattice QCD[S. Syritsyn et. al. arXiv:1111.0718 PoS(Lattice 2011)]

RBC/UKQCD: gauge fields2+1 flavors

domain wall fermions

MILC: gauge fields2+1 flavorsasqtad fermions

Angular momentum

Momentum faction

Puzzle: Why the difference from

experiment?Excited state contamination in nucleon structure

[J. Green et. al. arXiv:1111.0255 PoS(Lattice 2011) 157]

A20u-

d , B20u-

d , C20u-

d

mπ = 297 MeV A20 B20 C20

0.0

0.1

0.2

0.3

0.4

0.5

A20u-

d , B20u-

d , C20u-

d

mπ = 355 MeV A20 B20 C20

0.0

0.1

0.2

0.3

0.4

0.5

A20u-

d , B20u-

d , C20u-

d

Q2 [GeV2]

mπ = 403 MeV A20 B20 C20

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0


Moments of structure functions

Alexandrou et al. arXiv:1303.6818


The Proton Spin• What is the contribution of the quark spin to

the spin of the proton?

• EMC (1988) Q2 = 10 GeV2 ΔΣ = 0.00(24)

• SMC (1998) Q2 = 5 GeV2 ΔΣ = 0.13(17)

• Quarks contribute very little to the spin of the proton!

• ΔΣ should be 1 if all the proton spin is due to the spin of the quarks

• Spin crisis

ΔΣ = Δu + Δd + Δs


The Proton Spin

• The quark angular momentum can be computed on the lattice

•

• A and B are the generalized form factors of

ΔΣ = Δu + Δd + Δs

[LHPC: Hagler et. al. ‘03] [QCDSF: Hagler et. al. ‘03][Mathur et. al. ‘00]

[Ji,’98]

Gi(Q2) =

a1

1 +�

kbk⇥k

(14)

⇥ =Q2

4M2p

(15)

GnE(Q2) =

A

1 + B⇥GD(Q2) (16)

GD(Q2) =1

1 + Q2/⇥2(17)

⇥2 = .71GeV2

⇥d2�T

(2�)2e�i�T ·b (18)

1

2=

1

2�⇤ + �g + Lz (19)

1

2=

1

2�⇤ + Lq

z + Jgz (20)

�(x, b)

Jqz =

1

2[A20(0) + B20(0)] (21)

Gi(Q2) =

a1

1 +�

kbk⇥k

(14)

⇥ =Q2

4M2p

(15)

GnE(Q2) =

A

1 + B⇥GD(Q2) (16)

GD(Q2) =1

1 + Q2/⇥2(17)

⇥2 = .71GeV2

⇥d2�T

(2�)2e�i�T ·b (18)

1

2=

1

2�⇤ + �g + Lz (19)

1

2=

1

2�⇤ + Lq

z + Jgz (20)

�(x, b)

Gi(Q2) =

a1

1 +�

kbk⇥k

(14)

⇥ =Q2

4M2p

(15)

GnE(Q2) =

A

1 + B⇥GD(Q2) (16)

GD(Q2) =1

1 + Q2/⇥2(17)

⇥2 = .71GeV2

⇥d2�T

(2�)2e�i�T ·b (18)

1

2=

1

2�⇤ + �g + Lz (19)

1

2=

1

2�⇤ + Lq

z + Jgz (20)

�(x, b)

or

Oµ⇤ = q̄�{µ�D⇤} q = Tµ⇤ (22)


Proton SPIN

• Quark orbital angular momentum almost zero

• Disconnected diagrams are missing

0 0.1 0.2 0.3 0.4 0.5 0.6mπ [GeV]

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Lu

ΔΣu / 2

Ld

ΔΣd / 2

μ = 2 GeV

[J. Green et. al. arXiv:1111.0255


Computational Needs

Costtraj =

"✓fm

a

◆4 ✓Ls

fm

◆3 ✓Lt

fm

◆#5/4

·⇢B ·

✓MeV

m⇡

◆��+A

�(core hours)

Physical pion mass, a=0.075fm 1K lattices, 6fm box

Costs about 120 TFlop-Years

Gauge Field generation only

.....

Example:


Conclusions• Lattice QCD is a mature field

• Direct comparison with experiment is now possible for several observables

• Predictions are now emerging

• Hadron structure is now probed with lattice calculations

• LQCD calculations complement existing experimental program

• Improved precision is required

• Control systematic errors

• Potential impact to searches for new physics

• multi-Petaflop computing is required for precision calculations


Documents

Hadron Structure from LQCD - Oak Ridge Leadership ... · Hadron Structure from LQCD Kostas Orginos College of William and Mary JLAB OLCF April 29, 2013 Page 1 of 6 CASA Tracking Number: